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Journal of Statistics Education, Volume 20, Number 1(2012)

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Team-Based Learning in a Statistical Literacy Class

Katherine St. Clair

Laura Chihara

Carleton College

Journal of Statistics Education Volume 20, Number 1 (2012),

www.amstat.org/publications/jse/v20n1/chihara.pdf

Copyright © 2012 by Katherine St. Clair and Laura Chihara all rights reserved. This text may be

freely shared among individuals, but it may not be republished in any medium without express

written consent from the authors and advance notification of the editor.

Key Words: Team-based learning; Pedagogical strategy; Group work; Collaborative learning

Abstract

Team-based learning (TBL) is a pedagogical strategy that uses groups of students working

together in teams to learn course material. The main learning objective in TBL is to provide

students the opportunity to practice course concepts during class-time. A key feature is

multiple-choice quizzes that students take individually and then re-take as a team. TBL was

originally conceived by Larry Michaelsen (University of Central Missouri) for his business

classes and has proven to be especially effective in training medical students. In this paper, we

describe an adaptation of TBL for an undergraduate statistical literacy course.

1. Introduction

Using small groups to supplement traditional lectures is a valuable teaching technique in many

disciplines, including statistics. Students engage actively in the learning process, either by

working cooperatively on problems or discussing concepts (Garfield 1993; Keeler and Steinhorst

1995; Roseth, Garfield, and Ben-Zvi 2008). An instructor might use small groups casually and

not assign a grade to group work or worry about group composition. In a more structured use of

small groups, an instructor may dedicate a larger period of time to a group activity or worksheet,

and he may even form the groups. One pedagogical strategy that uses structured group work is

team-based learning. In this paper, we briefly describe the main features of team-based learning

and how we adapted this strategy for an undergraduate statistical literacy course.


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2. Team-Based Learning

Team-based learning (TBL) is a pedagogical strategy that uses groups of students working

together in teams during class to learn and apply course concepts. Unlike the use of small groups

described in the previous paragraph, teams are assigned permanently at the start of the course

and are held accountable throughout the term for both their individual and team efforts. Thus,

TBL falls under the broad definition of cooperative learning described in Garfield (1993).

The main learning objective in TBL is to provide students the opportunity to practice course

concepts during class-time. A TBL course is designed to move away from an instructor-centered

approach to learning where information flows from teacher to student to one where students

come to class prepared to apply the concepts from their readings. In this paper we describe the

main components of TBL, then discuss how we implemented TBL in a statistical literacy course.

Larry Michaelsen originally developed TBL for his business classes while at the University of

Oklahoma in the late 1970's. He was motivated by the enrollment pressures in his department

and wanted a way to effectively use small groups and active-learning in lecture halls of 120 plus

students. He came up with a teaching strategy that has four essential ingredients (Michaelsen,

Knight, and Fink 2004):

Teams The teams, which are formed by the instructor, are large (5-7 students), diverse

and permanent for the duration of the class. This team structure is designed to spread

weak and strong students across all teams which, with properly crafted in-class activities,

will also let the stronger students test their understanding of a topic as they explain it to

the weaker students in their team during an activity.

This structure should also motivate the weaker students to come prepared to contribute to

the team activity and not always be the team-member who has not done the needed

reading prior to class. The permanent structure of teams is designed to increase

communication and trust between team members and, as the class progresses, encourage

more open conversations between all team members, not just the confident and talkative

students on a team. These well-developed teams can tackle more challenging problems

than individuals or newly formed groups.

Accountability Students must be accountable for the quality of their individual and

group work. In particular, to make team-based collaboration effective, a student's

contribution to the success of the team must be part of the course grade.

Feedback Students must receive frequent and timely feedback from the instructor to

assess both individual and team learning. Feedback on an in-class activity can take many

forms such as simultaneously reporting answers to a question or giving students and

teams immediate feedback while they work through quiz questions. Immediate feedback

during group activities is also a key to the development of a successful team since the

most vocal or confident student in a team is not always the team member with the correct

answer. In Michaelsen's experience, once students realize that the most vocal student is


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not always the one with the correct answer, he [Michaelsen] saw quieter team members

begin to assert themselves.

Assignment design Group assignments must promote both learning and mutual team

development. "In most cases, team assignments generate a high level of interaction if

they require teams to use course concepts to make decisions that involve a complex set of

issues and enable teams to report their decisions in a simple form" (Michaelsen and

Sweet 2008). They note that well-designed activities usually satisfy the "4 S's" criteria:

significant question or problem, same assignment, specific choices, and simultaneous

reporting. They also advise that instructors should avoid assignments in which teams can

divide up the tasks among team members.

In Michaelsen's implementation of TBL, a key feature is the Readiness Assessment Process

(RAP): a course is organized into four or five major modules or units, and before each module

students are required to read ahead in the textbook on this material. To ensure that the class has

done the required reading, each student takes a multiple-choice quiz individually (Individual

Readiness Assessment Test, or iRAT), turns in their answers, then re-takes the quiz as a team

(Team Readiness Assessment Test, or tRAT). Team members must discuss each question and

come to a consensus on the answer. They then use an Immediate Feedback Assessment

Technique (IF-AT) card (Figure 1) on which they scratch off their choice for the correct answer.

These sheets provide instantaneous feedback as well as partial credit since they can continue to

scratch off choices until they arrive at the correct answer. A student's quiz score is then a

weighted average of the iRAT and tRAT scores. The RAP is designed around the four TBL

ingredients described above: individual accountability is assessed with the iRAT and team

development and accountability is assessed with the tRAT. The tRAT also provides students

with immediate feedback. Lastly, each quiz should be designed to assess knowledge of basic

course content, but also should be challenging enough to promote a high level of discussion

within each team.


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Figure 1. IF-AT scratch-off card

Students scratch off their choice for each question until they arrive

at the correct answer. Here, each problem is worth 4 points.

The IF-AT cards, made with options of four answer choices or five answer choices, are available

for purchase from the website: www.epsteineducation.com. (A set of 500 cards, each with 10

questions, costs $85.00.) Alternatively, if IF-AT cards are not available, an instructor can

instruct teams to rank their choices on a paper scorecard, then have teams grade their work with

an answer key that is provided at the end of the quiz. Though feedback would not be

instantaneous with each question, students would still receive nearly immediate assessment of

their understanding of the material. Instructors with access to a course management system and

computer labs could also build online quizzes that provide intermediate feedback to the student

teams.

After students take the quiz, class time is then spent on applications of the material. The primary

idea is to spend less class time lecturing on basic concepts and more class time letting students

learn how to apply the concepts.

TBL has been implemented successfully in medical education as well as in law and business

schools (Dana 2007; Mennenga and Smyer 2010; Vasan and DeFouw 2005). For instance, in an

article in Academic Medicine, Koles, Stolfi, Nelson, and Parmelee (2010) report on the impact of

TBL on the academic performance of second year medical students. On a high-stakes

pathology-based exam, the authors compared scores on questions related to content associated

with a TBL module (n = 250 students) to scores on questions unrelated to TBL modules (n = 462

students). Average score on TBL-related questions was significantly higher (p < 0.001) with the

weakest students being helped the most.

In the early 2000's, Harkness, Heckard, Buchanan, and Herbison (2002) and Harkness,

Buchanan, Heckard, and Rosenberger (2003) restructured the introductory statistics courses at

Penn State University by implementing RAT's to ensure student preparedness before a learning

unit. Students also worked on problem-based activities, often in a lab setting, in pairs or in

groups. While these courses had some components of Michaelsen's TBL, in particular, the RATs


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and in-class activities, it is not clear from their description whether these groups were permanent

for the duration of the course, or to what extent the team aspect was emphasized. Other TBL

strategies, such as the four S's of assignment design, are not mentioned in the Penn State

implementation.

3. TBL for a Statistical Literacy course

3.1 Background

Carleton College is a residential undergraduate liberal arts college of about 1800 students,

located in Minnesota. We offer two to three sections of our statistical literacy course every year.

The class size is typically between 30 to 35 students. Classes meet three times a week, 70

minutes on Mondays and Wednesdays, and 60 minutes on Friday, for nine and a half weeks. The

audience consists of humanities or fine arts students wanting to satisfy a graduation requirement,

as well as political science or sociology students taking the course as a prerequisite for a research

methods course. Calculus is not a prerequisite for the course.

The course focuses on statistical concepts with emphasis on understanding and interpretation of

statistical information, especially in the context of media reports and scholarly articles. The

technical demands are minimal: some basic probability, calculating z-scores, 95% confidence

interval for a proportion and the chi-square test statistic for a 2x2 table. We cover most of the

material in the textbook Seeing Through Statistics by Jessica Utts (2005). The students use the

statistical software program S+ (through the graphical user interface) to perform exploratory data

analysis.

3.2 Implementation

Our implementation of TBL for our statistical literacy course has all of the main ingredients of

TBL discussed in Section 2. The one alteration that we made was in the timing of the RAT

quizzes. In Michaelsen's original conception of TBL, the RAP occurs at the beginning of a new

module or unit with students taking the RAT to ensure that they have the basic background skills

needed to start applying the new concepts. We decided, however, that we wanted the quizzes to

assess more than the basic concepts in each unit, so we have made a crucial change by

administering the quizzes after having covered the material (typically one quiz every two

weeks). As indicated below, we utilize short online posts or quizzes to motivate class readiness.

Despite this modification, we feel that we are still able to capture the true spirit of TBL.1 In what

follows, we describe the basic design of our statistical literacy course and provide more details

about the some of the team activities and RAT quizzes used in our course.

On the first day of class, we explain the team-based learning concept and have the students take a

practice tRAT quiz. We then explain that their course grade will be a weighted average of one

midterm, a final exam, a data analysis project, participation, homework and the RAT quizzes

(Table 1).

1Though we administer the quizzes after covering a block of material, we will continue to use the acronym RAT.


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Table 1. Typical grading scheme

RAT quizzes (4) 25%

One midterm 25%

Final Exam 25%

Participation 10%

Report 12%

Homework 3%

The participation grade is based on attendance, pre-class posts to Moodle (a course management

software), and the student's contribution to their team. The midterm, final, data analysis project

and homework grades are based on individual efforts whereas the participation and RAT quizzes

grades have both an individual and team component.

In order to pass the course (C- or better), students must earn a passing grade on the individual

components of their grade. If and only if this criterion is met do we then factor in the team quiz

scores into their course grade. This policy is enacted to alleviate the concern that good students

often have about group work: weak or less industrious students riding on the coat-tails of their

stronger or better motivated classmates (i.e. "I did all the work but everybody got the same

grade"). We stress this policy throughout the term.

On the second day of the term, we form the teams of size five. We start by randomly assigning

students to teams, then we usually make some adjustments to ensure the teams are balanced with

respect to factors such as gender, class year, and major. These teams, which are permanent

assignments for the term, meet in class each day that is not an exam or computer lab day.

Students are required to prepare for class by reading ahead in the book on material that will be

covered in the next class. While the team-oriented structure of the class does encourage students

to actually do this reading, we still find it useful to implement individual checks of student

preparedness. Thus, to ensure that students have done the assigned reading, we check student

preparedness using the Moodle course website. One term we required students to post questions

or comments on the material on Moodle prior to coming to class. Moodle posts are factored into

each student’s individual participation grade. We structure our lecture around the questions and

comments submitted by the students. Typically, we lecture for about 20 to 30 minutes before

breaking into team activities. After receiving mixed feedback from students on these posts, that

the required posting encouraged reading but was not seen as a valuable learning tool to the

students, we switched to requiring students to take short quizzes on Moodle prior to class. These

three-question quizzes test basic content knowledge and are used to assess individual student

preparation. The quizzes also provide feedback to students prior to class about their grasp of

basic material. Instructors can then use quiz results to structure their lecture for that day and

scores become part of the student's individual grade.

3.2.1 Activities

As mentioned above, on a typical day, we start with a 20 to 30 minute lecture, then have the

students move into their groups for activities. We attempt to design many of our activities to


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have the "4 S's" criteria discussed in Section 2. The following describes an activity that

illustrates the 4 S’s idea.

Example 1: We provide the students with a newspaper article or a portion of a journal article.

After giving them some time to read through the material, we pose several multiple choice

questions about the reading to the teams. (We project the questions on a screen using

Powerpoint slides).

For instance, we give the students a 2007 news article describing a study in the United Kingdom

on a group of 10,000 government workers who were tracked for several years. In this study,

researchers found that those who did not get enough sleep were more than twice as likely to die

of heart disease compared to those who did get enough sleep. We ask: Which conclusion can be

made from this study?

A. This was a retrospective study and the populations being compared were those who did

and those who did not get enough sleep.

B. This was a prospective study and the populations being compared were those who did

and those who did not get enough sleep.

C. This was a prospective study and the populations being compared were those who died

from a heart attack and those who did not.

D. This was a retrospective study and the populations being compared were those who died

of heart attack and those who did not.

E. This was a case-control study and the controls were those who did not die of a heart

attack and the cases were those who did die of a heart attack.

After giving the students some time to discuss the question with their teammates, we instruct

each team to write down their answer on mini whiteboards. On cue, they simultaneously raise

their whiteboards so that all the students can inspect the responses. We then choose a team and

ask them to defend their choice. This is done to avoid "answer drift" (Michaelsen and Sweet

2008) where later responding students change or modify their responses based on what has been

said before, even if what was said before is incorrect. Simultaneous reporting forces every team

to make a decision before they know the pattern of responses of the other teams.

For problems whose answers cannot be reduced to a simple choice, we might send team

representatives to the blackboard to simultaneously report their answer. The following

True/False question is an example that can use this type of reporting.

Example 2: True or False. If the boxplot of a data set is symmetric, then the stem-plot of the

data set will also be symmetric. If true, justify your response; if false, provide a counterexample.

Another option for simultaneous reporting is the "gallery walk" (Michaelsen and Sweet 2008):

teams write answers on large easel paper, then post these sheets on the wall. Students walk

around the room to inspect the work, using post-it notes to make comments or ask questions.


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In all of the examples above, the in-class discussions that ensue are lively and motivate the

students to keep up with the material so that they may participate. These activities also provide

immediate feedback to students so that they do not leave class with misconceptions about the

material covered for that day.

Other in-class activities, that may or may not involve simultaneous reporting, include running

simulations or analyzing portions of journal articles. For technical topics such as basic

probability or the normal distribution, we hand out worksheets and have the teams work

collectively on the problems. We walk around the room to answer questions though, in general,

students help each other out and do not require much input from us. When most of the teams

have completed their worksheet, we choose one team to put the solutions on the blackboard. We

can then use this time to clarify any particularly difficult ideas or common misconceptions. See

the Appendix for a sample activity on understanding surveys and a sample worksheet on

hypothesis tests.

All team activities are done in class. This forestalls a common complaint that students have

about the difficulty in scheduling meeting times with their team members outside of class.

3.2.2 Quizzes

Approximately every two weeks (three to four chapters), we administered the quizzes with

fourteen multiple choice questions, each worth four points. First each student takes the quiz

individually. A student can earn partial credit by allocating the four points per problem in any

way s/he wishes (see Figure 2). For example, if a student is confident that the correct choice is

"C," he would place all 4 points under "C." But in a situation where a student is fairly certain the

answer is "A," but is hesitant to rule out "D," she could allot 3 points to "A" and 1 to "D." The

students appreciate earning partial credit on a multiple-choice quiz. More importantly, allowing

for partial credit paves the way for discussion when the students re-take the quiz as a team.

Teams are less likely to determine an answer by majority rule if individuals within a team

displayed uncertainty in their answer by splitting points between two or more options.


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Figure 2. Individual quiz answer sheet

Student can allocate 4 points in any manner he/she wishes. The

circled choice indicates the correct response and the right column

gives the points earned for each question.

We allot about 20 to 30 minutes for the individual quizzes after which the students turn in their

answer sheets and move into their groups to retake the quizzes as a team using the IF-AT forms

(Figure 1).

Sample question: A newspaper publishes a poll that says of 1010 Americans surveyed, 69%

support the death penalty with a 3% margin of error.

A. If we repeatedly sample 1,010 Americans, in about 95% of these samples we would get a

sample proportion between 66% and 72%.

B. We are 95% confident that between 66% and 72% of Americans support the death

penalty.

C. We are 95% confident that between 66% and 72% of the people in our sample support

the death penalty.

D. There is a 95% chance that between 66% and 72% of Americans support the death

penalty.

E. There is a 95% chance that between 66% and 72% of Americans in our sample support

the death penalty.

The discussions during the team quizzes are lively and intense. The students compare their

answers with their teammates and when there are discrepancies, go through a thoughtful give-

and-take, weighing the possible choices. The team scores are high---usually in the 90% range.

The table below is typical: it displays the statistics for one quiz (56 points possible). For


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instance, in Team 6, the average of the five individual scores was 54.3% (the highest individual

score was 75%), yet with the students working together, the team achieved a score of 98.2%.

Table 2. Team scores (percentage) on one quiz (out of 56 total points).

Team

1 2 3 4 5 6 7

Average individual score 69.2 73.7 81.3 71.8 61.1 54.3 64.3

Team Score 98.2 96.4 100 100 91.1 98.2 91.1

Average weighted score 87.7 88.4 93.4 90.1 80.6 82.8 77.9

In general, the team score is higher than the individual score of any given team member. In six

TBL courses, there have been only a few instances where an individual scored higher than the

team. The difference was small and did not affect the course grade of the individual.

As we noted earlier, a student's score for a quiz is a weighted average of the individual score and

his or her team scores (typically 35% individual, 65% team).

4. Discussion

We have found team-based learning to be an effective teaching strategy that focuses on students

practicing or applying statistical concepts in class. Although we spend some time lecturing on

course content, we expect students to learn the basic concepts on their own and devote most of

the class time on team assignments. By assessing students on both individual work and team

work, students are motivated to come to class prepared and engage in the group activities.

Students have been very positive about team-based learning. Between the two authors, we have

used TBL six times in the statistical literacy course. One of us (St. Clair) tabulated student

responses in two sections. Of 50 respondents, 94% liked the TBL format. In addition, 76%

thought the amount of lecturing by the professor was adequate, while 20% thought it was too

much and only 4% thought it was too little.

Students comment that they enjoy working on teams ("Loved teams! This is weird because I do

not normally like team work. In this class team work helped to understand the problem"), and

they appreciate the immediate feedback that they receive from the in-class activities ("I liked that

we were able to get instant feedback and teach one another"). Because in-class activities

required that each team produce something, an answer, a graph, etc., "I was motivated to prepare

for class every day because I did not want to let my teammates down."

Still, there are challenges in TBL. Weaker students still struggle with technical material and can

feel too intimidated by the other team members to ask for help. In this case, the teachers need to


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intervene and encourage the student to come to office hours for additional instruction.

Occasionally, a team may have one member who will not engage with the rest of the group

regardless of prodding and warning about the participation grade. By chance one team may end

up with all very strong students. We have had instances where one group regularly finishes the

entire activity 10 minutes before the rest of the class. We have not found a satisfactory way to

solve this dilemma, though the students appear to be happy to spend the time chatting about non-

class matters.

Faculty often worry that by spending more class time on activities rather than lecturing, less

material will be covered. We have not found this to be the case. One of us (Chihara) has taught

this course in a traditional lecture style as well as with TBL, and covered the same set of

chapters. However, the initial set-up of TBL does require time and effort by the instructor: the

entire course must be reconfigured, assignments or activities must be designed and multiple-

choice quizzes must be written.

Despite these challenges and problems, the overall satisfaction level of the students and

instructors is high. Students learn good habits such as reading the material before coming to

class; they mention that time goes by much more quickly than when listening to lectures. We,

the instructors, enjoy the high level of energy in the class and getting to know the students as we

walk around the room to answer questions or clarify concepts.

With any new pedagogical technique or strategy, it takes a leap of faith to make a radical change

in one's course design. At this point, we do not have any data for comparing student outcomes in

TBL versus non-TBL statistical literacy courses. We believe that team-based learning is an

exciting option for the statistical literacy course and potentially, for other statistics courses as

well (for instance, the introduction to statistics course taught at the level of De Veaux, Velleman,

and Bock 2009). Multiple choice questions for use in simultaneous reporting can still be written

for the more technical courses. Example 3 shows a multiple choice question that would be

suitable for a more technical course.

Example 3: Suppose nationally, about 90% of houses in any given city have smoke detectors.

Let p denote the true proportion of houses with a smoke detector in any given city. Suppose in

city A we have a random sample of n = 400 houses with ˆ 0.94p and a 95% confidence interval

(0.916, 0.964) and in city B, n = 4000, ˆ 0.92,p 95% confidence interval (0.911, 0.929).

Suppose we wish to test H0: p = 0.9 versus HA: p ≠ 0.9.

Question: For which city would the test be more statistically significant?

We also believe that team-based learning could successfully be implemented in much larger,

traditionally lecture style statistics courses. Harkness et al. (2003) demonstrated the

effectiveness of an active-learning and collaborative approach for large introductory level

statistics courses at Penn State University. The classes met as a whole (about 240 students) once

a week (RAT's were administered in this setting) and then broke up into smaller groups for

computer-mediated workshops with both undergraduate interns and graduate teaching assistants

helping out. Many other disciplines have successfully used TBL in large classroom settings

(Lasserre 2009; Clark, Nguyen, Bray and Levine 2008). Michaelsen et al. (2004) offer many


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suggestions for TBL in large classes such as distributing handouts or collecting assignments in

team folders to shorten materials-handling time, and re-emphasizing the importance of

simultaneous rather than sequential reporting of results when dealing with many teams. We

encourage interested instructors to read the book Team-Based Learning (Michaelsen et al. 2004)

and visit the Team-Based Learning Collaborative website http://www.teambasedlearning.org to

learn more.

http://www.teambasedlearning.org/


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Appendix: Sample Materials

Simultaneous Reporting Activity: Understanding Surveys

Understanding Surveys

Laura Chihara

Public Policy Polling (PPP)

Students are first asked to read about Public Policy Polling, a major polling company.

http://www.publicpolicypolling.com/aboutPPP/about-us.html

PPP claims that Interactive Voice Response (IVR) reduces interviewer bias to zero by using a

recorded voice, thus eliminating the live human interviewer. The person surveyed records his/her

answers by pressing keys on the phone keypad ("Press 1 for agree, 2 for disagree…"). Which of

the following are disadvantages of IVR over a live phone interviewer?

(I) No ability to verify identity of speaker on the phone.

(II) Respondents desire to please.

(III) Age related response rate.

(IV) Higher break-off rate (hang ups).

(A) II ; (B) III; (C) III and IV; (D) I, III, IV; (E) All of the above.

"IVR technology…allows us to complete surveys faster, usually in one evening." This seems to

suggest that PPP does not put in a lot of effort in callbacks - attempts to reach the respondent

another day/time if there is no answer. Gallup will try from 3 to 7 times over several days to

reach somebody.

Thus, compared to Gallup polls, surveys conducted by PPP may be

(A) less biased because PPP will not annoy people with lots of phone calls.

(B) more biased because PPP will have more women and older citizens in their sample.

(C) less biased because they survey everybody at the same time of day.

PPP uses a voter registration database for their sampling frame for most political surveys. For

pre-election surveys on the Obama-McCain presidential race last fall:

(A) It is unlikely that there was any bias as long as PPP used a scientific sampling method to

draw their sample.

(B) PPP polls may have underestimated support for McCain.

(C) PPP polls may have underestimated support for Obama.

Questions

The Sierra Club is sponsoring a survey in which several questions will be asked. Which survey

design (i.e. question order) would they most likely prefer (A or B)?

(A) i. Have the recent increases in gas prices had or not had an impact on your family’s budget?



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ii. Do you support or do you not support drilling for oil in Alaska’s National Wildlife Refuge

(ANWAR)?

(B) i. Do you support or do you not support drilling for oil in Alaska’s National Wildlife Refuge

(ANWAR)?

ii. Have the recent increases in gas prices had or not had an impact on your family’s budget?

Two poll questions from 2005

(Harris) Do you think that the law should allow doctors to comply with the wishes of a dying

patient in severe distress who asks to have his or her life ended, or not?

(Pew Research) In some states, it is legal for doctors to prescribe lethal doses of drugs that a

terminally ill patient could use to commit suicide. Do you approve or disapprove of laws that let

doctors assist patients who want to end their lives in this way?

The responses were

(A) 70%, 29%,1% in one poll and

(B) 46%, 45%, 9% in another (Yes or Approve, No or Disapprove,

No Response/Don’t know). Which was most likely the outcome for the Harris poll?

Which wording is the best?

(A) Would you say you are very likely, fairly likely, or not likely to vote in the national elections

this coming November?

(B) This coming November, how likely are you to vote in the national elections? Would you say

you are very likely, fairly likely, or not likely?

(C) Which of the following categories best describes how likely you think you are to vote in the

national elections this coming November: very likely, fairly likely, or not likely?

Validity and reliability

An analyst is interested in Northfield's Target business climate in January. Every day at 2pm, he

counts the number of cars in the parking lot and finds the average for the month. He will do this

every January for several years.

(A) This measurement is valid and reliable.

(B) This measurement is not valid but reliable.

(C) This measurement is valid but not reliable.

(D)This measurement is not valid nor reliable.


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Example Activity: Hypothesis tests

Where team is sent to the blackboard to present their responses.

Math 115 Chihara 1

Worksheet-Hypothesis tests

Example 1. Suppose researchers conduct an experiment to see if ultra-marathoners could reduce

respiratory infections by taking 600 milligrams of vitamin C daily. They find that 65% of the

runners in the placebo group report the development of symptoms of upper respiratory tract

infection after the race. This is significantly more (P< 0:01) than what the vitamin C

supplemented group reports (38%).

Write down the hypotheses being tested.

Explain the conclusion (p-value) of this study to somebody who hasn't had statistics.

Example 2. Here is an excerpt from a journal article:

(a) write down the null hypothesis.

(b) is the author's statement consistent with the statistical finding?

From “Adolescent Sexual Behavior in the Two Ethnic Minority Samples: The Role of Family

Variables” (Miller, Forehand, and Kotchick, 1999), “The number of times adolescents reported

having intercourse correlated negatively with the age of first intercourse (r = -.15; p < 0:01).”


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Example 3. Suppose a researcher conducts a one-sided hypothesis test and at the 05 level,

rejects the null hypothesis. If instead, this had been a two-sided hypothesis, would the researcher

come to the same conclusion?


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Math 115 Chihara 2

Example 4. The National Highway and Transportation Safety Administration (NHTSA) gives

automobile tires temperature grades (A, B, C) to indicate heat resistance – the ability to

withstand high temperatures that might cause blow-outs and tread separations.

The minimum grade acceptable is a C. Suppose a tire manufacturer is concerned that one of their

models doesn't meet the minimum requirements for a "C".

The engineers conduct an experiment to test this:

H0: Tires do meet the minimum requirements for heat resistance.

H: Tires do not meet the minimum requirements for heat resistance.

What are the Type I and Type II errors, and what are their consequences? (Explain in the context

of this problem.)

Example 5. “Beneficial effects of high dietary fiber intake in patients with Type 2 diabetes

Mellitus” (Chandalia, Abhimanyu, Lutjohann, von Bergmann, K., et al., 2000 ).

“The high-fiber diet reduced plasma total cholesterol concentrations by 6.7 percent (P=0.02),

triglyceride concentrations by 10.2 percent (P=0.02), and very-low-density lipoprotein

cholesterol concentrations by 12.5 percent (P=0.01).”

Write down the null and alternative hypotheses.

What Type of error could the researchers have made in this study? What might be the practical

consequence of this error?


18

Acknowledgements

We thank JSE editor John Gabrosek, a JSE associate editor and the referees for their helpful

comments.

References

Chandalia, M., Abhimanyu G., Lutjohann, D., von Bergmann, K., et al. (2000), "Beneficial

effects of high dietary fiber intake in patients with type 2 diabetes mellitus," The New England

Journal of Medicine, 342, 19, 1392-1399.

Clark, M. C., Nguyen, H. T., Bray, C., and Levine, R. (2008), "Team-based learning in an

undergraduate nursing course," Journal of Nursing Education, 47, 3, 111-117.

Dana, S. W. (2007), "Implementing Team-Based Learning in an Introduction to Law Course,"

Journal of Legal Studies Education, 24, 59-108.

De Veaux, R., Velleman, P., and Bock, D. (2009), Intro Stats, 3rd Edition, Boston, MA, Pearson.

Garfield, J. (1993), "Teaching statistics using small group cooperative learning," Journal of

Statistics Education [online], Vol. 1, No. 1. Available at

http://www.amstat.org/publications/jse/v1n1/garfield.html.

Harkness, W., Heckard, R., Buchanan, P., and Herbison, M. (2002), "Elementary statistics: The

Penn State model," in American Statistical Association Proceedings of the Section on Statistical

Education, pp. 1364-1373.

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http://www.amstat.org/v3n2/keeler.html


19

Mennenga, H. A. and Smyer, T. (2010), "A model for easily incorporating team-based learning

into nursing education," International Journal of Nursing Education Scholarship [online], Vol.7,

Iss. 1, Article 4. Available at http://www.bepress.com/ijnes/vol7/iss1/art4.

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Transformative Use of Small Groups in College Teaching, 1st Edition, Sterling, VA., Stylus

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Roseth, C., Garfield, J., and Ben-Zvi, D. (2008), "Collaboration in learning and teaching

statistics," Journal of Statistics Education [online], Vol. 16, No. 1. Available at

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Journal of Medical Education, Vol. 39, No. 5, 524.

Laura Chihara

Department of Mathematics

Carleton College

Northfield, MN 55057

[email protected]

507-222-4065 (office)

507-222-4143 (fax)

Katherine St. Clair

Department of Mathematics

Carleton College

Northfield, MN 55057

[email protected]

507-222-4193 (office)

507-222-4143 (fax)

http://www.bepress.com/ijnes/vol7/iss1/art4


http://www.amstat.org/v16n1/roseth.html

mailto:[email protected]



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